Transistor amplifier with conjugate input and output circuits



22. 1953 L. A. MEACHAM TRANSISTOR AMPLIFIER WITH CONJUGATE INPUT AND OUTPUT CIRCUITS Filed June 28. 1950 FIG 6 INVENTOR L. A. M54 CHAM Patented Dec. 22, 1953 UNITED STATES FATENT OFFICE TRANSISTOR AMPLIFIER WITH CONJU GATE INPUT AND OUTPUT CIRCUITS York Application June 28, 1950, Serial No. 170,727

4 Claims.

This invention relates to transistor amplifiers and particularly to improved transistor amplifier circuits.

A principal object of the invention is to obtain strictly one-way amplification of signals by means of a transistor amplifier.

Related objects are to render the input impedance of a transistor amplifier circuit independent of its load, and to render its output impedance independent of the impedance of the signal source which drives it.

The three basic transistor amplifier circuits, namely grounded base, grounded emitter, and grounded collector, are described, and their properties summarized in Some Circuit Aspects of the Transistor by R. M. Ryder and R. J. Kircher published in the Bell System Technical Journal for July 1949 at page 367 (vol. 28). As examination of the mathematical expressions for input and output impedance as published by Ryder and Kircher shows, the input impedance depends in each case on the load and the output impedance depends on the sourceimpedance. As a result, in the design and construction of a multistage amplifier, it is impossible to treat each of the several stages as if it were alone. On the contrary, the properties of each stage depend on the characteristics of the other stages of the group. This places restrictions on the designer and limits the ease with which a transistor amplifier may be treated as a circuit element for general purposes. Ryder and Kircher also show that, in general, the backward gain of a transistor amplifier is not zero.

Now it happens that certain features of the transistor behave differently in the diiierent ampliiier circuits. As a principal example, consider the effects on the input impedance, in the case of each of the three basic circuits, of an increase in the current-multiplication factor'alpha which, as explained by Ryder and Kircher on page 375 of the aforementioned publication, isapproximately equal to the ratio of the mutual resistance Tm of the transistor to its collector resistance it. In the grounded base circuit, the input impedance may be reduced and may even be made to pass through zero and become negative by increasing the positive feedback, as by increasing current-multiplication factor. Qn the other hand, a similar increase of feedback. in the grounded emitter circuit tends to increase the magnitude of the input impedance, and may even cause it to reach and pass an infinite value,

thereafter becoming negative. Similar opposing tendencies are found with respect to the output impedance as between the grounded base circuit and the grounded collector circuit.

The present invention turns these opposing tendencies to positive account by balancing one against the other. In one embodiment, a circuit configuration is provided which is a mean between the grounded emitter circuit and the grounded base circuit and in which the tendencies of the one are balanced against the corresponding opposing tendencies of the other. It turns out, when the balance is correct, that the output circuit is conjugate to the input circuit with the results that the input impedance is independent of the load impedance while the output impedance is independent of the impedance of the driving source. In addition, the input impedance is also independent of the current-multiplication factor alpha, and the backward transmission of the amplifier network is zero.

In a'second embodiment, a circuit configuration is provided which is a mean between the grounded base circuit and the grounded collector circuit. Here again the output circuit is conjugate to the input circuit in such a way that the output impedance is independent of the impedance of the driving source and the backward transmission of the network as a whole is zero.

Each of the foregoing embodiments involves the neutralization of the effects of feedback which are inherent in one of the parent circuits by equal and opposite effects of feedback inherent in the other. Extension of thisprinciple to an amplifier network comprising a pair of transistors connected in push-pull leads to a crossneutralization of the positive feedback voltage of each member of the pair by an oppositely phased voltage derived from the other member of the pair.

The circuits of the invention are evidently useful wherever strictly unilateral transmission is desired, and also wherever it is important that the impedance presented by an amplifier network at one pair of terminals be independent of the impedance connected to the opposite pair oi terminals; for example, in the design of 2. cascade amplifier network or in the association of an amplifier with a network which is sensitive to changes in magnitude of the impedances connected thereto.

The invention will be fully apprehended from the following detailed descripticn of preferred embodiments thereof taken in connection with the appended drawings, in which;

Fig. 1 is a schematic circuit diagram showing one embodiment of the invention;

Fig. 2 is an equivalent circuit diagram of Fig. 1;

In Fig. 3, Fig. 2 is redrawn as a bridge circuit;

Fig. 4 is a schematic circuit diagram of second embodiment of the invention;

In Fig. 5, Fig. 4 is redrawn as a bridge circuit;

Fig. 6 is a schematic circuit diagram showin the application of the principles of Fig. 1 to an amplifier network comprisinga pair of transistors connected in push-pull; and

Fig. '7 is a schematic circuit diagram showing the application of the principles of Fig. 4' to an amplifier network comprising. a pair of transistors connected in push-pull.

Referring now to the drawings, Fig. 1 shows a transistor comprising a semiconductive body I having a base electrode 2, an emitter electrode 3 and a collector electrode 4 making contact therewith, a signal source represented by the idealized generator VG and its internal resistance R connected to the emitter 3 and to the base 2, respectively, and a load R1. in circuit with the collector 4. Operating bias potentials are supplied for the collector by a first battery 5 and for the emitter by a second battery 6. Padding resistors R and Rh may be inserted in series with the emitter and base electrodes, respectively, if desired.

In accordance with the invention, there is provided between the emitter electrode 3 and the base electrode 2 a voltage divider network which is preferably, though by no means necessarily, reactive. Thus, a tapped coil 9 is shown, while a pair of condensers connected in series would serve equally well at low frequencies. The coil 9 will of course fail to support a voltage at the very low frequencies and the condensers will fail to support it at the very high frequencies; wherefore if the performance and operation are contemplated over the whole gamut of frequencies, a tapped resistor may be preferred. Because of the power dissipated in the resistor, a reactive voltage divider such as the coil 9 which is as nearly as possible an ideal coil, of negligible loss and unity coupling between the two sides, is in general preferable.

In accordance with the invention, the collector 4 is returned not to the base electrode 2 as in the case of the grounded base circuit, nor to the emitter electrode 3 as in the case of the grounded emitter circuit, but to an intermediate point of the voltage divider impedance element, such as the tap II! on the coil 9. On the hypothesis that the total number of turns of the tapped coil 9 is proportional to unity and that the tap is located at a point which is removed from the base electrode end of the coil by a fraction n of the turns and from the emitter end of the coil by a fraction (1n) of the turns, and with the aid of the simplified equivalent circuit diagram, Fig. 1a, the circuit equations may be formulated. In Fig. 2 the polarizing batteries are omitted and the transistor (including padding resistances Re and Rb if they are used) is replaced by the equivalent group of resistances Te, rs and To and the mutual impedance element Tm, all of which quantities and terms have the significance given them in the Ryder-Kircher publication above referred to. The circuit equations so obtained are as follows:

from which, in the customary manner, the circuit determinant A may be formed by cross-multiplication of the coeiiicients of the currents is and in, its magnitude being given by Comparing this expression with the expressions given by Ryder and Kircher for the grounded base circuit on page 376 and for the grounded emitter circuit on page 378, it may be seen that the Expression 3 is more complex than either one, and partakes of the nature of each; that when 12:0 it reduces to the expression for the grounded base circuit, while for n l it reduces to the corresponding expression for the grounded emitter circuit; and that, in short, it represents a compromise between the two.

Following known methods of circuit analysis, and utilizing the definition of input impedance, namely RH= .-"-RG it may be shown that mwcr) +m(m+m+Rr) -nm. (5)

- while the output impedance R22, correspondingly defined, is given by Now it turns out that if n is given the value and this value is substituted in (3) and (5) above, these expressions are greatly simplified, reducing to Equation 5a shows that the input impedance is now independent of the load RL, and of Tm, which is a measure of the current multiplication factor, alpha. Equation 6:: shows that the output impedance is independent of the source impedance Re.

Furthermore, defining the forward power gain as the ratio of the power delivered to the load to that supplied to the input when the source impedance and the input impedance are matched,

iL V */4R (8) and using conventional methods to substitute for ii a there results 5 Similarly it can be shown that the backward power gain reduces to zero; i. e.

With a typical transistor, signal source, and load, having the following parameter values:

re=390 ohms rt=140 ohms n=19,000 ohms rm=34,000 ohms RG=500 ohms RL=10,000 ohms the proportioning of the voltage divider impedance element in accordance with Equation 7 gives b r.+rb

Rl1=Te+Tb=53O ohms R22=Tc-7l(7m?'e) =10,100 ohms GF=54 10 log GF=17.3 db

then the two diagonals of the bridge are conju gate to each other. In accordance with the wellknown principles of conjugacy, a voltage applied to the vertical diagonal of the bridge, as by application of the signal of the external source VG, causes no current to flow through the horizontal diagonal. The current of the source divides at the upper junction point, a first fraction flowing through the resistances Te and 'n; in series and another fraction flowing through the ratio arms ln and n in series. By making the impedance of the voltage divider impedance element 9 large, it can be arranged that the second fraction of the generator current is so small as to be practically negligible, so that the impedance presented to the generator is substantially equal to Te+Tb in accordance with Equation a. This impedance is independent of the load impedance EL, of the mutual resistance Tm, which measures the current-multiplication factor alpha, and also of the collector contact resistance Tc. In short, the impedance presented by the bridge to the generator VG is independent of all of the circuit elements which are contained in the conjugate diagonal of the bridge.

This does not mean that the load R1. carries no current. 011 the contrary, the generator current flowing through the emitter resistance Te results in the generation of an effective internal electromotive force by the transistor which, as

flows through the load resistance RL, and forward transmission is obtained. The power gain associated with this forward transmission is given by Equation 9.

It may also be seen by examining the bridge network of Fig. 3 that the backward transmis sion of the system is zero. Thus, suppose an external signal E to be generated across the terminals of the load RL by any cause whatsoever. This may upset the potential dinerence between the two ends of the horizontal diagonal and it may, indeed, cause current to flow through all of the arms of the bridge. However, inasmuch as the horizontal diagonal has been adjusted to a condition of conjugacy with the vertical diagonal, this disturbance causes no current to flow through the external resistor R Thus the baclz ward transmission of the system is zero.

This does not mean that the impedance loolzing into its output terminals is infinite. On the contrary, as stated above, the introduction or: such an electromotive force in the load causes current to flow through the horizontal diagonal and through all of the bridge arms, and the effect of this behavior is to produce an output in1pedance R22 whose magnitude is given by (dc) above. This may now be shown as follows.

Subject to the restriction that the voltage divider impedance element 5 is a perfect or ideal coil with unity coupling between the two sides, then this postulated electromotive force produces no voltage drop across either part of the coil, and the mesh equation for the upper mesh of the bridge becomes simply E+Tmie=0+Te e+TcUri-iii) (11) From Kirchoffs first law for the junction point of Te, Tb and To,

ie+ib+ic=0 (12) while, when the bridge is balanced,

ic7 'e=ib7'b (13) Eliminating is and it by substituting (l2) and (13) into (11), and then dividing through by is gives grounded base circuit and the grounded collector circuit. Here a voltage divider impedance element which, as before, is preferably an ideal coil 1 l with unity coupling between the two parts but may instead be a tapped resistor or a pair of condensers or separate inductances in series, is connected between the collector electrode :3 and the base electrode 2, while the emitter electrode 3, in series with which the external signal source symbolically represented by the voltage generator VG and its internal resistance Hg, is returned to some point on the coil I i which is intermediate between its ends. As before, padding resistors Rb and Be may be added in series with the base and the collector, respectively. Fig. 5 is the same circuit, redrawn to bring out the fact that the load R1. and the signal source Vc are in the horizontal diagonal and the vertical diagonal, respectively,

of a Wheatstone bridge; and that when this 'bridge'is balanced by proportioning the two parts of the coil II in the ratio of the base resistance to the collector resistance, the load and source are respectively conjugate to each other. Thus,

if the two parts of the voltage divider impedance element H are proportional to n and to 1n'. respectively, establishment of the relation put impedance of the network, namely the im- 1 pedance looking from the load terminals toward the transistor, is independent of the impedance Rg of the signal source.

To carry out the invention, it is of course not necessary that a perfect adjustment of the two parts of the voltage divider impedance elements be made exactly in the ratio of the contact resistances of the transistor. On the contrary, at the sacrifice of a small amount of power and gain, a resistor can be added in series with the base, the emitter, or the collector, as desired in order to increase or reduce the ratio given by Equation '7 or 14 and so facilitate the achievement of the balance of the invention without the fabrication of a special coil having an exactly located tap. In particular, an external emitter resistance Re and an external base resistance Rb have been included in the circuit of Fig. 1 to make the base resistance as padded bear some desired relationship to the emitter resistance as padded: for example equality therewith, and so to adjust the ratio However, economy is by no means the only consideration in the choice of n. For example, referring to Equation So, if 'n, is one-half, and if, as is generally the case, Tm is equal to or greater thanzrc, while Te is negligible in comparison to 'Im, the output impedance R22 becomes zero or negative, and instability may result. It is to be understood that the principles of the invention are not to be applied without regard to stability considerations. It will also be recognized that choice of n aifords a convenient means of establishing a desired value of R22 in accordance with Equation 6a, or of B11 in accordance with Equation 501.. By resorting to padding resistors Re, Rb or Be or a combination of them, n or n can be chosen within wide limits while still satisfying Equation '7 or 14 as the case may be.

Fig. 6 shows the application of the principles of the invention to an amplifier comprising a pair of transistors I, 2|, connected in push-pull. The signal is applied by way of an input transformer having a center-tapped secondary winding 28 to the emitters 3, 23, of the two transistors in opposite phase and is withdrawn from the two collectors 4, 24 likewise in push-pull, byway of an output transformer 3| whose primary windin is center tapped at the point 32. The two center taps 30, 32 are connected together. Here, however, portions of the secondary winding of the input transformer 29 which serve as the voltage divider impedance element do double duty for the '30, 32 are connected together.

upper transistor I and for the lower one 2!. Thus, for the upper transistor, the lower portion of the voltage divider impedance element, proportional to n in Fig. 1, runs from the point I; to the center tap 30 of the secondary winding 29 while the upper portion, proportional to 1n, runs from the center tap 30 to the point 2. Similarly, for the lower transistor the first portion of the coil, proportional to 11,, runs from the point at to the center tap 30 while the second portion, proportional to 1n, runs from the center tap 30 to the point a.

Biasing voltages may be applied to the electrodes of the transistors of Fig. 6 by connection of the negative terminal of a battery 25 to the center tap 32 of the output transformer 3!, the opposite terminal of the battery 25 being connected by way ofindividual isolating resistors and blocking condensers to the emitters and bases of the two transistors.

With this arrangement the points (1 and 2) move outward to the coil end terminals 6 and a, respectively, under the special conditions that the emitter resistance is equal'to the base resistance, whether intrinsically or by the addition of padding resistors, so that the ratio is equal to one-half. Under this condition the whole of the secondary winding of the input transformer 29 does double duty for the upper transistor I end for the lower one 2!. In the general case when the ratio in question is not equal to one-half, then the center tap 38 of the input winding 29 divides the portion b-e of this winding which interconnects the emitter 3 and the base 4 of the upper transistor i into two portions whose ratio is equal to the ratio of the base resistance to the emitter resistance; while similarly, the same center tap 30 divides the portion l-d, of the input winding 29 which interconnects the base 22 with the emitter 23 of the lower transistor 2! in the ratio of its base resistance to its emitter resistance.

The same principles may be applied to a pushpull transistor amplifier network which embodice the features of Figs, 4 and 5, as shown by Fig. 7. Here the two ends of an input winding 25 are connected to the emitters 3, 23 of two transistors I, 2!, while the two ends of an output winding 3| are connected to the collectors 4, 2 of the same two transistors. Each winding is provided with a center tap, and the center taps Further, each portion of the output winding 31 is provided with an upper intermediate tap, located between the center tap and. upper end of the winding and with a lower intermediate tap located between the center tap and the lower end of the winding. The base 2 of the upper transistor i is returned to the lower intermediate tap while the base 22 of the lower transistor 2| is returned to the upper intermediate tap. Biasing voltages may be derived from a battery 25 and applied by way of isolating resistors and blocking condensers to the electrodes in the manner shown. Now, the center tap 32 of the output winding 3! divides that portion of the output winding which interconnects the base of the upper transistor with its collector in accordance with Equation 14; i. e., in the ratio of the transistor base resistance to its collector resistance, while, similarly, the same center tap 32 divides that portion of the output winding which interconnects the 'base of the lower transistor with its collector in the ratio of the base resistance of the lower transistor to its collector resistance. Thus, as in the case of Fig.6, portions of the winding lying immediately above and below the center tap do double duty for the two transistors.

What is claimed is:

1. A translating network which comprises a transistor having a semiconductive body, an emitter electrode, a collector electrode and a, base electrode making contact with said body, a voltage divider impedance element interconnecting the base electrode with the emitter electrode and having a tap connected to a point thereof intermediate its ends, the collector electrode being connected to said tap, an input circuit including a source connected in shunt with said element, and an'output circuit including a load connected in series with the collector electrode.

2. Apparatus as defined in claim 1 wherein the ratio of the impedances of the two parts of the voltage divider impedance element into which it is divided by the tap, is substantially equal to the ratio of the base resistance of the transistor to the emitter resistance of the transistor.

3. Apparatus as defined in claim 1 wherein the voltage divider impedance element is a lowloss coil, the portions of said coil on either side of said tap being closely coupled to one another magnetically.

References Cited in the file of this patent UNITED STATES PATENTS Number Name Date 1,884,675 Heising Oct. 25, 1932 1,968,104 Roberts July 31, 1934 2,003,282 Black June 4, 1935 2,170,645 Peterson Aug. 22, 1939 2,226,694 Buschbeck Dec. 31, 1940 2,247,218 Braaten June 24, 1941 2,524,035 Bardeen et al Oct. 3, 1950 2,541,322 Barney Feb. 13, 1951 2,556,286 Meacham June 12, 1951 2,556,296 Rack June 12, 1951 2,609,459 Bergson Sept. 2, 1952 

